Quantum phase transitions, frustration, and the Fermi surface in the Kondo lattice model

The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.Comment: 9 pages, 8 figure

Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach

We develop a general approach to the nonequilibrium dynamics of quantum impurity systems for arbitrary coupling strength. The numerical renormalization group is used to generate a complete basis set necessary for the correct description of the time evolution. We benchmark our method with the exact analytical solution for the resonant-level model. As a first application, we investigate the equilibration of a quantum dot subject to a sudden change of the gate voltage and external magnetic field. Two distinct relaxation times are identified for the spin and charge dynamics.Comment: 5 pages, 5 figure

Adiabatic pumping through a quantum dot in the Kondo regime: Exact results at the Toulouse limit

Transport properties of ultrasmall quantum dots with a single unpaired electron are commonly modeled by the nonequilibrium Kondo model, describing the exchange interaction of a spin-1/2 local moment with two leads of noninteracting electrons. Remarkably, the model possesses an exact solution when tuned to a special manifold in its parameter space known as the Toulouse limit. We use the Toulouse limit to exactly calculate the adiabatically pumped spin current in the Kondo regime. In the absence of both potential scattering and a voltage bias, the instantaneous charge current is strictly zero for a generic Kondo model. However, a nonzero spin current can be pumped through the system in the presence of a finite magnetic field, provided the spin couples asymmetrically to the two leads. Tunneling through a Kondo impurity thus offers a natural mechanism for generating a pure spin current. We show, in particular, that one can devise pumping cycles along which the average spin pumped per cycle is closely equal to $\hbar$. By analogy with Brouwer's formula for noninteracting systems with two driven parameters, the pumped spin current is expressed as a geometrical property of a scattering matrix. However, the relevant %Alex: I replaced topological with geometrical in the sentence above scattering matrix that enters the formulation pertains to the Majorana fermions that appear at the Toulouse limit rather than the physical electrons that carry the current. These results are obtained by combining the nonequilibrium Keldysh Green function technique with a systematic gradient expansion, explicitly exposing the small parameter controlling the adiabatic limit.Comment: 14 pages, 3 figures, revised versio